Rogers_CH8

1. Assuming that a path has no colliders on it, what is the difference between a path being Open and Closed?

• An open path is a path where the arrows only lead from the treatment variable to the outcome variable (causality flows from treatment to outcome)

• A closed path is a path where any of the arrows lead toward the treatment variable (not all causality flows from treatment to outcome)

2. Consider the below generic causal diagram.

1. List every path from X to Y.

• X - A - Y
• X - B - Y
• X - B - D - Y
• X - C - D - Y
• X - C - D - B - Y

2. Which of the paths are front-door paths?

• X - A - Y

3. Which of the paths are open back-door paths?

• X - B - Y
• X - B - D - Y
• I think X - C - D - Y is not “open” (but is back door) because of the collider C

4. What variables must be controlled for in order to identify the effect of X on Y? (only list what must be controlled for, not anything that additionally could be controlled for).

• B has an effect on X and Y, so that should be controlled because it may be increasing the perceived effect of X on Y.
• I’m not sure about E, I think as long as the sample allows for sufficient randomness about E then we shouldn’t need to control for it?

3. Consider the research question: Does having higher income cause better health?

1. Draw a causal diagram depicting the data generating process for this relationship with 5-10 variables on it.

• 

2. Identify the Front Door paths.

• income - food - health
• income - housing - health
• income - stress - health
• income - stress - smoking - health

3. Identify the Back Door paths.

• income - pre-existing condition - health
• income - city - stress - health
• income - city - stress - smoking - health

4. Identify the paths that represent direct effects.

• Is this asking paths which have a direct effect on health? if so:
• smoking - health
• stress - health
• food - health
• housing - health
• pre-existing condition - health

5. Identify the Good Paths and the Bad Paths.

• good paths:

• income - food - health

• income - housing - health

• income - stress - health

• income - stress - smoking - health

• bad paths:

• income - pre-existing condition - health

• income - city - stress - health

• income - city - stress - smoking - health

4. Which of the following describes a causal path where all the arrows point away from the treatment?

• Front Door Path

5. Consider the figure below, which depicts the relationship between teaching quality, number of publications (e.g., articles, books), and popularity among scholars and students in a population of professors.

1. What type of variable is Popularity in one path on this diagram?

• popularity is a collider here because two variables have arrows going into it and it has no arrows going out from it

2. Discuss what would happen if you controlled for Popularity.

Controlling for a collider closes a path.

6. Consider the figure below, which depicts the relationship between a pandemic-related lockdown and an economic recession. The research question of interest is: Does a pandemic-related lockdown cause recession?

1. Write down all the paths in the diagram from Lockdown to Recession. To make our lives simpler (there are a lot of paths in this diagram), ignore any path that goes through Stimulus.

• lockdown - recession
• lockdown - unemployment - recession
• lockdown - unemployment - priorEconomy - recession
• lockdown - priorEconomy - recession
• lockdown - priorEconomy - unemployment - recession

2. List all of the paths that are Front Door Paths.

• lockdown - recession
• lockdown - unemployment - recession

3. What would happen if we controlled for unemployment?

• Controlling for unemployment closes the following:

• lockdown - unemployment - recession

• lockdown - unemployment - priorEconomy - recession (collider path, so controlling unemployment actually opens the path?)

• lockdown - priorEconomy - unemployment - recession

• (I’m realizing that the last two paths are basically the same paths but ordered differently. Then are they the same paths or two separate paths?)

4. Is it possible to measure each of the variables adequately?

• I’d imagine so. The only one that seems tricky is lockdown, I can only imagine measuring this as a binary variable (lockdown Y/N), though maybe it could be YearsInLockdown

5. Can you think of any variables and paths not depicted in the diagram that may be relevant to identify the answer to the research question? List at least one and no more than three.

• vaccinated and hasDisease

• lockdown - vaccinated - hasDisease - unemployment - recession

• logic is, lockdown causes more people to get vaccinated, vaccination effects disease status, which effects unemployment and finally recession status

7. Consider the question: Does obtaining a higher education improve income? Think of a couple of examples of Bad Paths in a causal diagram depicting the data generating process for this research question.

• bad paths:
• education - parentalIncome - income
• education - age - income